Properties of Functions

1103025601

Level: 
A
The function \( f \) is given by the graph. Which of the following statements is true?
The function \( f \) has a minimum and a maximum at every \( x \) of its domain.
The function \( f \) has the minimum at \( x=-6 \) and the maximum at \( x=3 \).
The function \( f \) has the maximum at \( x=3 \) and it has no minimum.
The function \( f \) has neither a minimum nor a maximum.

1103028409

Level: 
A
The function \( f \) is given by the graph. Which of the statements about the domain and the range of the function \( f \) is true?
\( D(f) =[-3;4]; H(f)=[-2;2)\cup(2; 3]\cup\{5\} \)
\( D(f) =[-3;1)\cup(1; 4]; H(f)=[-2; 2)\cup(2; 3] \)
\( D(f)=[-3;4]; H(f)=[-2;5] \)
\( D(f) =[-3;4]; H(f)=[-2;3]\cup\{5\} \)

1003028407

Level: 
B
Paul went by car from Ostrava to Olomouc for a business trip. There he spent \( 50 \) minutes at the meeting and then he went back the same way. Paul covered the distance of \( 98\,\mathrm{km} \) from Ostrava to Olomouc in \( 64 \) minutes. The distance back he covered in \( 66 \) minutes. Suppose the recording of the travelled distance and the time spent on the business trip started when Paul left Ostrava. Dependence of this distance on the time describes the function \( s(t) \). Distance is in kilometres and time is in hours. Which of the following statements about the domain and the range of the function \( s \) is correct?
\( D(s)=[0;3] ; H(s)=[0;196] \)
\( D(s)=[0;196] ; H(s)=[0;3] \)
\( D(s)=[0;3] ; H(s)=[0;98] \)
\( D(s)=\left[0;\frac{13}6\right] ; H(s)=[0;196] \)

1003028406

Level: 
A
Suppose the function \( f \) is given completely by the next table. \[ \begin{array}{|c|c|c|c|c|c|c|c|}\hline x&-3&-2&-1&0&1&2&3 \\\hline y&-4&4&-4&4&-4&4&-4 \\\hline \end{array} \] Which of the following statements about the range of the function \( f \) is true?
\( H(f)=\{-4; 4\} \)
\( H(f)=\{-3;-2;-1;0;1;2;3\} \)
\( H(f)=[-4;4] \)
\( H(f)=(-4;4) \)

1003028405

Level: 
A
Suppose the function \( f \) is given completely by the next table. \[ \begin{array}{|c|c|c|c|c|c|c|c|} \hline x&-2&-1& 0&1&2&3&4\\\hline y&0&1&0&2&3&5&4 \\\hline \end{array} \] Which of the following statements about the domain of the function \( f \) is true?
\( D(f)=\{-2; -1;0;1;2;3;4\} \)
\( D(f)=\{0;1;2;3;4;5\} \)
\( D(f)=\{-2;-1;0;1;2;3;4;5\} \)
\( D(f)=[-2;4] \)

1003028404

Level: 
B
Let \( f(x)=\frac{\sqrt{x+3}}{x^2-25} \). Which of the statements about the domain of the function \( f \) is true?
\( D(f)=[-3; 5)\cup (5;\infty) \)
\( D(f)=(-3;5)\cup(5;\infty) \)
\( D(f)=(-\infty;-5)\cup(-5;5)\cup(5;\infty) \)
\( D(f)=(-\infty;-5)\cup(-5;-3)\cup(-3;5)\cup(5;\infty) \)